Uncovering Heterogeneity Using Tree-Based Machine Learning

Tree-based ML

data(iris)

iris %>% 
  select(Sepal.Length, Sepal.Width, Species) %>% 
  head() %>% 
  kable()

Tree-based ML

Tree-based ML

• The maximum value of Gini(Ω) is 1/2, corresponding to a graph where p = 0.5, indicating that the sample data is evenly split between classes.

Hetergentous Treatment Effects

• Assumptions:
  • Unconfoundedness: whether or not a person is treated is determined completely by their observable characteristics.
  • Overlap: at every point of the covariate space we can always find treated and control individuals.

Causal Tree

• Adaption:
  • to partition the data to minimize differences in potential outcomes rather than minimizing differences in observed outcomes.
  • however, we do not observe the causal effect for any unit.
• Honest Estimation:
  • performance of the tree is based on treatment effect heterogeneity rather than predictive outcome accuracy.

Causal Tree

Apply Causal Tree with simulation:

tree <- simulation %>% 
  causalTree(
    y ~ x1 + x2 + x3 +x4,
    data = .,
    treatment = simulation$treatment,
    split.Rule = "CT",
    cv.option = "CT", 
    split.Honest = T, 
    cv.Honest = T, 
    split.Bucket = F, 
    xval = 5, 
    cp = 0, 
    minsize = 20, 
    propensity = 0.5
  )

Tree plot:

rpart.plot(tree)

Empirical Application

• Question: heterogeneous effects of college on reducing low-wage work for subgroups defined by different variables.

• shiny app